The character for trời (eng: sky), which is basically a <天> on top of a <上>, looks very similar to the Jurchen character for "sky"; the Jurchen character has a <丄> on the bottom instead of <上>, although both mean the same thing. The Jurchen character is read as abka.

In order to view the Nôm characters, you may need to install the Hán Nôm fonts A and B. If not, here's an image of it. It's colour coded, Black = Original Chinese character (Hán), Blue = Invented Vietnamese character (Nôm).

There probably are some similar invented characters but I doubt the number would be particularly high. Vietnamese is linguistically unrelated to the Jurchen language and unlike the Jurchen characters, the Vietnamese Chữ Nôm characters pretty much follow the Chinese conventions of character creation and many Chữ Nôm characters are easily mistaken to be Chinese in origin.

Here's a song I translated called Tan Biến (To Disappear):

If Vietnamese still used Chữ Nôm as its official writing system, then it'd probably surpass Chinese in terms of overall difficulty to learn.